Augmented Graph Fourier Transform (AuGFT)

Supplemental materials for article "Realization of DiGraph Filters Via Augmented GFT"

AuGFT

Supplemental materials for article "Realization of DiGraph Filters Via Augmented GFT"

• H. Kitamura, H. Yasuda, Y. Tanaka and S. Muramatsu, "Realization of DiGraph Filters Via Augmented GFT," 2023 IEEE International Conference on Image Processing (ICIP), Kuala Lumpur, Malaysia, 2023, pp. 2885-2889, doi: 10.1109/ICIP49359.2023.10222618.
• Abstract: This study proposes a filtering method for directed graph (digraph) signals. In order to realize digraph filtering, a novel graph Fourier transform (GFT), – Augmented GFT (AuGFT) –, is proposed by defining an Hermitian adjacency matrix. Although there has been the same method to give the adjacency matrix of digraphs, this study defines a novel digraph Laplacian. The existing digraph Laplacian does not give the graph signal variation considering the edge directions, while the novel one does. This paper introduces three important ideas. The first is the definition of a novel degree matrix to give the novel digraph Laplacian. The second is to decompose the symmetric and skew-symmetric components of the novel digraph Laplacian independently into their spectral components. The third is, based on the decomposition, to augment the conventional GFT for digraphs as an invertible real-valued dictionary. The new GFT is shown to provide a practical form of real-valued digraph filtering. The significance of the proposed method is verified through simulations of signal filtering on digraphs.
• URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=10222618&isnumber=10221892

Acknowledgement

This work was supported by JSPS KAKENHI Grand Numbers JP21H04596 and JP22H00512.